Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

Saúl Díaz Infante Velasco, Silvia Jerez, Benito Chen-Charpentier

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Abstract

In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.
Original languageSpanish (Mexico)
Pages (from-to)153
Number of pages164
JournalMathematical Biosciences
Volume299
DOIs
StatePublished - 8 Mar 2018

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